REDISCOVERING THE TRUE THEORY OF THE I-CHING UNDER THE LIGHT OF MATHEMATICS: 5,000 Years Lost · Found Again (Bilingual Edition)

This work presents a unified, formal mathematical framework for the foundational figure system of the I-Ching (Yi Jing) based on binary algebra and discrete state transitions. Demonstrating that the core architecture of the I-Ching operates as a power function of two, D = T(2ⁿ) as n → ∞, the treatise establishes the Thien Tich Toc Constant Law: vaμₙ = 2ⁿ − 1. At every structural level n, bit-complementary pairs sum to this invariant parametric constant, forming the essential diametrical symmetry of the Earlier Heaven Bagua (TTBQ). Rigorous analysis demonstrates that the Later Heaven Bagua (HTBQ) violates binary continuity and breaks complementary equilibrium (yielding chaotic sums 7, 10, 10, 1), while King Wen’s "Double-Trigram Theory" is mathematically insufficient as a progressive generative law. To resolve these historical discontinuities, this work reconstructs the omitted intermediate levels: the Sixteen Figures (Level 4, 2⁴ = 16 states, vaμ₄ = 15) and the Thirty-Two Figures (Level 5, 2⁵ = 32 states, vaμ₅ = 31). Furthermore, the study introduces a dynamic discrete time-transformation function, D = T(2ⁿ, t), governed by bit-toggling operators (0 ↔ 1), and models the Infinite Figure State (Vô Cực Quái) as an unbounded asymptotic expansion: V = T(n) as n → ∞. The mathematical system is rigorously contextualized alongside Gottfried Wilhelm Leibniz’s binary calculus (1701–1703), modern Boolean AI Logic (XOR, AND, OR, NOT), Vedic cosmology, and Buddhist Dependent Origination (Pratītyasamutpāda). - Original Thought & Mathematical Formulation by: Bùi Văn Nam (Sāmaṇera Minh Thoát).- English Edition by: Most Venerable Thích Minh Tâm (Bhikkhu Visuddhamma).- Edition: Bilingual Vietnamese – English Complete Pre-press Edition (2026).